Monoid of self-equivalences and free loop spaces

Félix, Yves;Thomas, JC.
(2004) Proceedings of the American Mathematical Society — Vol. 132, n° 1, p. 305-312 (2004)

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  • Félix, YvesUCLouvain
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  • Thomas, JC.
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Abstract
Let M be a simply-connected closed oriented N-dimensional manifold. We prove that for any field of coefficients lk there exists a natural homomorphism of commutative graded algebras Gamma : H-*(Omega aut(1)M) --> H*(M-S1) where H-*(M-S1) = H*+N(M-S1) is the loop algebra defined by Chas and Sullivan. As usual aut(1)X denotes the monoid of self-equivalences homotopic to the identity, and OmegaX the space of based loops. When lk is of characteristic zero, Gamma yields isomorphisms H-(1)(n+N) (M-S1) congruent to (pi(n)(Omegaaut(1)M) x lk)(boolean OR) where +(infinity)(l=1) H-(l)(n)(M-S1) denotes the Hodge decomposition on H*(M-S1).
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Félix, Y., & Thomas, JC. (2004). Monoid of self-equivalences and free loop spaces. Proceedings of the American Mathematical Society, 132(1), 305-312. https://doi.org/10.1090/S0002-9939-03-07018-7 (Original work published 2004)